Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 1)
1
Which trigonometric ratio is used to find the angle when you know the adjacent and the hypotenuse sides?
Answer
(B)
Cosine
2
In a triangle, if you know the lengths of two sides and the included angle, which rule would you likely use to find the length of the third side?
Answer
(B)
Cosine Rule
3
What is the defining feature of a right-angled triangle that allows the direct use of Pythagoras' theorem?
Answer
(B)
It has one angle that is 90 degrees.
4
What is the formula for calculating the length of the diagonal of a cuboid with sides a, b, and c?
Answer
(B)
d = √(a² + b² + c²)
5
What do you need to know to calculate the third side of a right-angled triangle?
Answer
A
D
6
What is/are the correct ways to determine angles when using trigonometry?
Answer
A
B
D
7
What is the name given to the side of the triangle next to a given angle (that is not the hypotenuse)?
Answer
(B)
Adjacent
8
What information do you need to use the cosine rule to find the length of a side?
Answer
(C)
Two sides and the included angle.
9
In a three-dimensional problem involving finding lengths or angles, which of the following is/are useful tools?
Answer
A
B
D
10
What trigonometric function utilizes the ratio of Opposite/Adjacent?
Answer
(C)
Tangent
11
If two sides of a triangle measure 5 cm and 8 cm, and the included angle is 60 degrees, what is the length of the third side (approximate)?
Answer
(C)
4.8 cm
12
Which trigonometric function uses the opposite side and the hypotenuse?
Answer
(A)
Sine
13
In the context of the given image, what is the significance of 'three-figure bearings'?
Answer
(C)
They provide a standardized way to express direction, measured from North.
14
What is the core purpose of studying trigonometry?
Answer
(B)
Investigating the relationships between angles and sides in triangles.
15
In order to calculate the area of a triangle, you require...
Answer
(A)
base & height or 2 sides and the included angle
16
What do you need to know to use the cosine rule to find an angle in a triangle?
Answer
(B)
All three sides
17
Which of the following must be true for the Pythagorean theorem to apply?
Answer
(B)
The triangle must have one angle equal to 90 degrees.
18
What trigonometric ratio involves the opposite and hypotenuse sides?
Answer
(A)
Sine
19
What information is required to use the formula Area = 1/2 * ab * sin C to find the area of a triangle?
Answer
(B)
The length of two sides and the angle between them.
20
In a right-angled triangle, what do you call the side *opposite* the right angle?
Answer
(C)
Hypotenuse
21
In a triangle ABC, if a = 10cm, b = 16cm, and C = 150°, what is the area of the triangle?
Answer
(A)
40 cm²
22
Which of the following is correct regarding the angle of elevation and angle of depression in the same diagram, assuming parallel lines?
Answer
(C)
Angle of elevation equals the angle of depression.
23
A boat sails 10 km due north and then 8 km in a south-easterly direction. To determine the final position of the boat you will need to consider:
Answer
(C)
Trigonometry and vector addition
24
How does the area of a triangle formula using sine relate to the area of a right triangle?
Answer
(C)
The formula works as sin(90°) = 1.
25
Which ratio represents the sides Opposite/Hypotenuse?
Answer
(A)
Sine
26
What is the purpose of the 'sine' function in the context of trigonometry?
Answer
(A)
To relate angles to side lengths in a right triangle.
27
If sin(x) = 0.6, what is the approximate value of x (in degrees)?
Answer
(B)
37°
28
If two sides of a right-angled triangle are 5cm and 12cm, what is the length of the third side?
Answer
(A)
13 cm
29
If the angle between sides a and b of a triangle is known, along with the lengths of sides a and b, which formula can be used to calculate the triangle's area?
Answer
(C)
Area = 1/2 * a * b * sin(C)
30
Which of the following is a correct statement related to the area of a triangle?
Answer
(A)
Area of a triangle = 1/2 * base * height
31
What is the name for the longest side of a right-angled triangle?
Answer
(C)
Hypotenuse
32
If sin(120°) = 0.866, then sin(60°) is:
Answer
(B)
0.866
33
Which trigonometric function can be used if given the lengths of all three sides and you are trying to find an angle?
Answer
(C)
Cosine
34
If a triangle has sides a = 4, b = 6, and angle C = 60 degrees, what is the length of side c (approximately)?
Answer
(B)
5.28
35
In trigonometry, what does the acronym SOH CAH TOA help to remember?
Answer
(B)
The formulas for the trigonometric ratios.
36
Which of the following is the correct formula to calculate the area of a triangle?
Answer
(B)
Area = 1/2 * base * height
37
Which of the following statements is/are correct about trigonometry ratios?
Answer
B
C
38
To find the area of a triangle, using the formula 1/2 * a * b * sin C, what information is needed?
Answer
A
B
39
If the height of a tree is 10 meters and the angle of elevation from a point on the ground to the top of the tree is 60 degrees, what is the approximate distance from the observer to the base of the tree?
Answer
(D)
5.77 meters
40
In a right-angled triangle, which side is adjacent to a given acute angle?
Answer
(C)
The side next to the angle (other than the hypotenuse).
41
If the angle of elevation is given and the height of an object is known, how can you find the horizontal distance to the object?
Answer
(C)
Using Tangent function
42
Which of the following statements are true about the sides of a right-angled triangle?
Answer
A
C
43
The angle of elevation from point A to the top of a tower is 30°. The distance from A to the tower's base is 100m. What is the tower's approximate height?
Answer
(B)
57.7 m
44
What does the 'hypotenuse' of a right-angled triangle refer to?
Answer
(D)
Both b and c
45
What is the value of sin(30°)?
Answer
(B)
1/2
46
What are the steps for solving the problem of using the ratios?
Answer
A
B
C
D
47
What is the meaning of the 'inverse' key on the calculator when solving a trigonometry problem?
Answer
(B)
To find the angle
48
What is the main focus of trigonometry?
Answer
(B)
Studying the relationship between angles and sides in triangles.
49
In which units are trigonometric functions usually measured?
Answer
(C)
Degrees or Radians
50
If two sides of a triangle are 7 cm and 9 cm, and the included angle is 60 degrees, what is the length of the third side (approximately)?
